Multiply the following complex numbers: $({i}) \cdot ({-5+3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({i}) \cdot ({-5+3i}) = $ $ ({0} \cdot {-5}) + ({0} \cdot {3}i) + ({1}i \cdot {-5}) + ({1}i \cdot {3}i) $ Then simplify the terms: $ (0) + (0i) + (-5i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 - 5)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 - 5)i - 3 $ The result is simplified: $ (0 - 3) + (-5i) = -3-5i $